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Estimating Multilevel Logistic Regression Models When the Number of Clusters is Low: A Comparison of Different Statistical Software Procedures

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  • Austin Peter C

    (Institute for Clinical Evaluative Sciences)

Abstract

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

Suggested Citation

  • Austin Peter C, 2010. "Estimating Multilevel Logistic Regression Models When the Number of Clusters is Low: A Comparison of Different Statistical Software Procedures," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-20, April.
  • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:1:n:16
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    Cited by:

    1. Giorgio Di Gessa & Karen Glaser & Debora Price & Eloi Ribe & Anthea Tinker, 2016. "What Drives National Differences in Intensive Grandparental Childcare in Europe?," Journals of Gerontology: Series B, Gerontological Society of America, vol. 71(1), pages 141-153.
    2. Diaz, Mireya, 2015. "Performance measures of the bivariate random effects model for meta-analyses of diagnostic accuracy," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 82-90.
    3. Bryan, Mark L. & Jenkins, Stephen P., 2013. "Regression analysis of country effects using multilevel data: a cautionary tale," ISER Working Paper Series 2013-14, Institute for Social and Economic Research.
    4. Kim, Tae Jun & Vonneilich, Nico & Lüdecke, Daniel & von dem Knesebeck, Olaf, 2017. "Income, financial barriers to health care and public health expenditure: A multilevel analysis of 28 countries," Social Science & Medicine, Elsevier, vol. 176(C), pages 158-165.
    5. Pau Baizan & Bruno Arpino & Carlos Eric Delclòs, 2016. "The Effect of Gender Policies on Fertility: The Moderating Role of Education and Normative Context," European Journal of Population, Springer;European Association for Population Studies, vol. 32(1), pages 1-30, February.

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